Mulvaney mostly meets with voters through weekly town hall meetings. Sometimes he brings with him a 30-minute PowerPoint presentation, full of bar graphs and fever charts depicting the growing federal deficit and the surging cost of health care. In January, Mulvaney added a chart on the automatic spending cuts, known as sequestration, which next year will total about $100 billion.

To him the numbers make sense. “In the greater scheme of things, they are not that big,” Mulvaney said.

But, every once in a while, a personal anecdote punctures his certainty. Earlier this month, a friend and former campaign volunteer stood up at one of the town hall meetings to tell Mulvaney…